René Magritte has inspired more book covers than any other visual artist. The first Magritte cover adorned Mary Potter's Useful Mathematics Workbook, published in Boston in 1939. The designer used a detail of Mental Arithmetic (1931; destroyed), in which a village of conventional houses with tiled roofs has been colonised by a cluster of gigantic white spheres, hemispheres and cuboids.

This eerie toytown image deftly prophesies what was about to happen in architecture – the colossal "pure forms" of Le Corbusier's modernism usurping more complex and cosy traditional forms. At the same time, the juxtaposition panders to the human need to find patterns and geometry in nature. We notice that the rising sun is also hemispherical, and that the pitched roofs of the houses are triangular: the similarities between the pure white forms and the rural idyll they find themselves in are as striking as the differences. Indeed, could not the sun simply be another hemisphere placed on the horizon? Here lateral thinking and seeing can render what initially seems alien to be archetypal and even natural; and it can in turn make the houses and trees seem cramped, gloomy and unhomely. Yet in Magritteville, the friction between forms never falters, never settles into a reassuring pattern. His sites – with their pathological neatness, cleanness, staticness – cannot be fully stabilised or surveyed. Mental Arithmetic defies conventional computation: here 1 + 1 = 2 and infinity.

A recent exhibition in Boston of Magritte-inspired book covers had 60 works of fiction and non-fiction, and could have featured many others (the curator Karl Baden now owns about 100). Examples include Germaine Greer's The Female Eunuch (the woman-as-nightdress, hanging from a rail); Michel Foucault's meditation on the picture of a pipe inscribed "This Is Not a Pipe"; Georges Simenon's Maigret's Pipe (a bowler-hatted man seen from the back); and Patrick Süskind's The Pigeon (a bowler-hatted man seen from the back with a pigeon perching on his hat). What appeals to publishers and readers is the epigrammatic spareness of Magritte's work, together with an almost heraldic clarity. You register the naively limpid image/word instantly, then do a double-take and are insidiously hooked – intellectually, if not emotionally. No less important is the fact that book titles and author names can be deposited in one of the many voids that punctuate his pictures. He leaves blank and blandly patterned zones into which all manner of mental furniture can be scattered.

René Magritte (1898-1967) was brought up in Hainault, Belgium's coal-mining region, the eldest son of a prosperous businessman (edible oils, stock cubes). He soon showed talent as an artist, which his father encouraged, and went to art school in Brussels in 1915. His mother was a depressive, with suicidal tendencies, and when René was 13 she drowned herself in the river at the back of their house. Magritte only ever spoke about her death to one close friend, years later. He said that when the body was dragged from the polluted waters several days later her face was covered by her nightdress. It was not known whether she had hidden her eyes with it before jumping in, or whether the river had "veiled her thus". The only feeling Magritte remembered was "intense pride at the thought of being the pitiable centre of attention in a drama".

The "drama" involving the nightdress sounds too good to be true, like a carefully contrived primal scene, ripe for Freudian analysis. It is surely a period piece, borrowed from a symbolist novel or painting, invented or imagined by Magritte to lend his mother romance and gravitas – and to endow himself with superhuman sang froid.

Veiled figures were a symbolist leitmotif. The Italian sculptor Medardo Rosso's Impression on the Boulevard: Woman with a Veil (1893) is the obvious example, yet all of Rosso's bust-length figures, mostly women and children, seem equally veiled. Their hiddenness adds to the sense of mystery, melancholy and melodrama. Comparable figures, now facing away from the viewer, and blank mannikin heads, are found in the work of Rosso's younger Italian contemporary Giorgio de Chirico, the discovery of whose paintings in the 1920s came as a revelation to Magritte, and set him on the path he was to follow for the best part of his career. Magritte was to make the suspiciously hidden head – obscured, turned, featureless, missing, beheaded, behatted – his own.

In the early 1920s, Magritte had been working his way steadily through cubism and futurism, subsidising himself by doing commercial art – something he would have to do until after the second world war, when he secured a New York dealer (examples of his commercial work will be included in the new Tate Liverpool show). In the mid-1920s, the recently formed French surrealists, and the German dadaists Max Ernst and George Grosz, were hailing De Chirico as a founding father, and Magritte was bowled over by a reproduction of De Chirico's Love Song in an art magazine. De Chirico showed Magritte how you could make resonant paintings by "collaging" together disparate still-life objects painted in a deadpan, hyper-real style, with distorted scale and spatial logic. Magritte said of the Italian leader of the Scuola Metafisica: "It was a new vision through which the spectator might recognise his own isolation and hear the silence of the world".

But whereas De Chirico situated his objects within plunging architectural perspectives inspired by early renaissance painting, Magritte's compositions tend to spread out laterally, as if belonging to an illustrated textbook or display cabinet. Abetting this lateral extension is his penchant for dividing pictures into stark, shifting sequences of square and rectangular compartments, akin to advertising hoardings or stage flats. It is a modernist reworking of the medieval polyptych format, where each saint or protagonist is isolated in its own framed panel. Magritte liked the format because of the feeling of potentially endless shuffling and unfolding.

Magritte's work is, in part, a joke at the expense of the classifying, bureaucratic mind. His drily preposterous pedantry makes one think of Flaubert's Bouvard and Pécuchet (1881), in which the eponymous copy-clerks seek to become experts in every conceivable subject solely by reading books, rather than consulting people with experience. The hapless autodidacts try to bottle preserves, plant trees, look after farm animals, practise medicine; they try to learn how to write a novel and how to have imagination. All their experiments end in disaster, and their home becomes a museum, choked with specimens. Eventually they give up and go back to being copy-clerks. Magritte's paintings look as though they might have been made by a well-meaning but over-zealous autodidact – and it's a consummate irony that they end up on the covers of so many self-help books.

Magritte moved to Paris in 1927 with his wife and frequent model Georgette and, although he gained the respect and admiration of André Breton and the surrealists, he never became part of the inner circle. It was a matter partly of geography – he could only afford to rent a flat in the suburbs – and partly of style. At this stage in its evolution, surrealism was dominated by semi-abstract "automatic" drawing, as epitomised by the work of André Masson and Joan Miró: beauty, as Breton said, was convulsive. It wasn't until the 1930s, with the ascendancy of surrealist sculpture and photography, and of Salvador Dalí, that Magritte's work fitted the bill. By that stage, however, he had already returned to Brussels, due to both the fallout of the 1929 Wall Street crash and a row with Breton over a crucifix worn by Georgette to a party. The violently atheistical Breton insisted she remove it, but Magritte sided with his wife.

Many of Magritte's most famous works were painted during his Paris stay. The False Mirror – a close-up of a left eye, with a cloudy sky where the iris should be – is both visionary and claustrophobic, for while the flying-saucer eye seems magically enlarged, the sky seems circumscribed (this later became the logo for CBS television). The Titanic Days (1928) is the most intelligently shocking of his images. A naked woman of heroic scale struggles with a clothed man who assails her from her left. But the man's figure is neatly cut off at the contour of the woman's body, so only the superimposed part of the man is depicted. What makes it so disturbing is the idea that he is an indissoluble, bespoke part of herself, an essential item both of her own wardrobe and her anatomy – a parasitical human corset. We can't tell whether this is simply a rape scene, or an internecine struggle between conjoined forces. They are both equal parts of a diptych folding in on itself. Picasso later tried a similar trick when he made his mesmerising image of his young mistress, The Dream (1932), with the left side of her sleeping head formed from a tumescent lilac penis.

Partly inspired by Miró (whose exhibition at Tate Modern runs concurrently) and by dadaism, Magritte started to incorporate words into his pictures, and the 40-odd word pictures he made in Paris constituted about a quarter of his output there. Foucault, appreciating the painstaking appearance of Magritte's joined-up handwriting, said it was written in "a script from the convent". The Key of Dreams (1930), made in several versions, is a classic example. A sequence of images, as if from a child's school book, each one isolated in a square frame, is spectacularly "mis-labelled" – so beneath a picture of a high-heeled shoe we read "the moon", beneath a jug "the bird" and so on.

A version of The Key of Dreams appeared on the front cover of John Berger's Ways of Seeing (1972). According to Berger, it demonstrates that there is an "always present gap between words and seeing". This is the message that countless conceptual artists have taken from Magritte's work. Yet it is far from clear this is what Magritte meant. The main inference we can draw is that dreams are meaningless, a random sequence of unfettered images and words to which there is no key. We can interpret This Is Not a Pipe in a similar way, for pipe tobacco is an addictive, perception-altering drug that inspires reverie. That is very much how the pipe is treated in The Philosopher's Lamp (1936), a grotesque self-portrait in which Magritte's nose is distended like an elephant's trunk and flops down into the bowl of the pipe he is smoking, as if to suggest the depths of his own addiction. He looks at us sidelong, sadly, well aware how pathetic and impotent he looks. A worm-like candle burns limply on a console table before him. Unlike the surrealists, Magritte is a reluctant dreamer. He wants to stay wide awake and in control. He wants reality and reason to prevail, and for affinities to be found between objects: he was an admirer of Goethe's novel Elective Affinities. A yearning for simple truths lies at the heart of his prosaic, deliberate painting style. The creative tension in his work stems from his chronic inability to keep a lid on himself and the world.

There is indeed something pathetic about Magritte's later work and career: from the 1930s an increasing part of his production was making copies of his most popular works, as well as forgeries of artists such as Picasso and Ernst, and portraits. When the Germans invaded Belgium in 1940, he decided that people needed cheering up and so, until 1947, he painted lurid soft-porn pastiches of late Renoir. In 1948, he tried his hand at a comic-strip fauvism – his "vache" (cow) paintings – before returning to making variations on his standard themes. He became famous for the first time in the late 1950s, when his classic work chimed with pop art, and later, with conceptual art. It was then that he marketed himself to the wider world as the "ordinary man in the bowler hat, suit and tie" who just happened to paint extraordinary pictures. At his death in 1967, this pose (sans bowler hat) was taken up with a vengeance by Gilbert & George. What the response to his laconic art will be these days, when beauty is both convulsive and garrulous (Tracey Emin), remains to be seen.

René Magritte: The Pleasure Principle is at Tate Liverpool from 24 June until 16 October 2011.